SOLUTION: {{{(a+b)x^2+(a-2b)x+k=(k-1)x^2+5x+3}}} In the equation above a, b and k are constants. If the equation is true for all real values of x, what is the value of a?

Algebra ->  Functions -> SOLUTION: {{{(a+b)x^2+(a-2b)x+k=(k-1)x^2+5x+3}}} In the equation above a, b and k are constants. If the equation is true for all real values of x, what is the value of a?      Log On


   

Question 1041073: %28a%2Bb%29x%5E2%2B%28a-2b%29x%2Bk=%28k-1%29x%5E2%2B5x%2B3
In the equation above a, b and k are constants. If the equation is true for all real values of x, what is the value of a?
Answer by ikleyn(52750) About Me  (Show Source):
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%28a%2Bb%29x%5E2%2B%28a-2b%29x%2Bk=%28k-1%29x%5E2%2B5x%2B3
In the equation above a, b and k are constants. If the equation is true for all real values of x, what is the value of a?
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The condition implies that

a +  b = k-1,   (1)
a - 2b = 5,     (2)
k      = 3.     (3)

First step to simplify gives

a +  b = 2,     (4)
a - 2b = 5.     (5) 

Distract (4) from (5). You will get

-3b = 3,  hence,  b = -3.

Then from (4) a = 2 - b = 2 - (-3) = 5.

Answer.  a = 5, b = -3,  k = 3.